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High School Math Calculus PRECALCULUS:GRAPHICAL,...-NASTA ED.

To estimate: The area of the region above the x -axis and under the graph of the given function from x = 0 to x = 5 . The area of the region above the x -axis and under the graph of the given function from x = 0 to x = 5 is 12.5 square units. Given information: A curve and the value of x ranges from 0 to 5 . Formula used: Area of rectangle = l × w Calculation: The given curve is partitioned into strips of rectangles. Area of each strip of rectangle can be calculated as below. The area of first rectangle from left is given below. Width of the rectangle is 1 and length of the rectangle is approximately 4 . Substitute 4 for l and 1 for w in the area of rectangle formula. Area = 4 × 1 = 4 Hence, the area of the first rectangle is 2 square units. The area of second rectangle from left is given below. Width of the rectangle is 1 and length of the rectangle is approximately 5 . Substitute 5 for l and 1 for w in the area of rectangle formula. Area = 5 × 1 = 5 Hence, the area of the second rectangle is 5 square units. The area of third rectangle from left is given below. Width of the rectangle is 1 and length of the rectangle is approximately 2 . Substitute 2 for l and 1 for w in the area of rectangle formula. Area = 2 × 1 = 2 Hence, the area of the third rectangle is 2 square units. The area of fourth rectangle from left is shown below. Width of the rectangle is 1 and length of the rectangle is approximately 0.5 . Substitute 0.5 for l and 1 for w in the area of rectangle formula. Area = 0.5 × 1 = 0.5 Hence, the area of the fourth rectangle is 0.5 square units. The area of fifth rectangle from left is given below. Substitute 2 for l and 1 for w in the area of rectangle formula. A r e a = 2 × 1 = 2 Hence, the area of the fifth rectangle is 2 square units Calculate the sum of areas of all the rectangles. 4 + 5 + 2 + 0.5 + 2 = 13.5 Hence, the area of the region above the x -axis and under the graph of the function from x = 0 to x = 5 is 13.5 square units.

To estimate: The area of the region above the x -axis and under the graph of the given function from x = 0 to x = 5 . The area of the region above the x -axis and under the graph of the given function from x = 0 to x = 5 is 12.5 square units. Given information: A curve and the value of x ranges from 0 to 5 . Formula used: Area of rectangle = l × w Calculation: The given curve is partitioned into strips of rectangles. Area of each strip of rectangle can be calculated as below. The area of first rectangle from left is given below. Width of the rectangle is 1 and length of the rectangle is approximately 4 . Substitute 4 for l and 1 for w in the area of rectangle formula. Area = 4 × 1 = 4 Hence, the area of the first rectangle is 2 square units. The area of second rectangle from left is given below. Width of the rectangle is 1 and length of the rectangle is approximately 5 . Substitute 5 for l and 1 for w in the area of rectangle formula. Area = 5 × 1 = 5 Hence, the area of the second rectangle is 5 square units. The area of third rectangle from left is given below. Width of the rectangle is 1 and length of the rectangle is approximately 2 . Substitute 2 for l and 1 for w in the area of rectangle formula. Area = 2 × 1 = 2 Hence, the area of the third rectangle is 2 square units. The area of fourth rectangle from left is shown below. Width of the rectangle is 1 and length of the rectangle is approximately 0.5 . Substitute 0.5 for l and 1 for w in the area of rectangle formula. Area = 0.5 × 1 = 0.5 Hence, the area of the fourth rectangle is 0.5 square units. The area of fifth rectangle from left is given below. Substitute 2 for l and 1 for w in the area of rectangle formula. A r e a = 2 × 1 = 2 Hence, the area of the fifth rectangle is 2 square units Calculate the sum of areas of all the rectangles. 4 + 5 + 2 + 0.5 + 2 = 13.5 Hence, the area of the region above the x -axis and under the graph of the function from x = 0 to x = 5 is 13.5 square units.

PRECALCULUS:GRAPHICAL,...-NASTA ED.

PRECALCULUS:GRAPHICAL,...-NASTA ED.

10th Edition

ISBN: 9780134672090

Author: Demana

Publisher: PEARSON

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Expert Solution & Answer

Chapter 11.2, Problem 9E

Solution

To estimate: The area of the region above the $x$ -axis and under the graph of the given function from $x=0$ to $x=5$ .

The area of the region above the $x$ -axis and under the graph of the given function from $x=0$ to $x=5$ is $12.5$ square units.

Given information:

A curve and the value of $x$ ranges from $0$ to $5$ .

Formula used:

Area of rectangle $=l×w$

Calculation:

The given curve is partitioned into strips of rectangles.

Area of each strip of rectangle can be calculated as below.

The area of first rectangle from left is given below. Width of the rectangle is $1$ and length of the rectangle is approximately $4$ .

Substitute $4$ for $l$ and $1$ for $w$ in the area of rectangle formula.

$Area=4×1=4$

Hence, the area of the first rectangle is $2$ square units.

The area of second rectangle from left is given below. Width of the rectangle is $1$ and length of the rectangle is approximately $5$ .

Substitute $5$ for $l$ and $1$ for $w$ in the area of rectangle formula.

$Area=5×1=5$

Hence, the area of the second rectangle is $5$ square units.

The area of third rectangle from left is given below. Width of the rectangle is $1$ and length of the rectangle is approximately $2$ .

Substitute $2$ for $l$ and $1$ for $w$ in the area of rectangle formula.

$Area=2×1=2$

Hence, the area of the third rectangle is $2$ square units.

The area of fourth rectangle from left is shown below. Width of the rectangle is $1$ and length of the rectangle is approximately $0.5$ .

Substitute $0.5$ for $l$ and $1$ for $w$ in the area of rectangle formula.

$Area=0.5×1=0.5$

Hence, the area of the fourth rectangle is $0.5$ square units.

The area of fifth rectangle from left is given below.

Substitute $2$ for $l$ and $1$ for $w$ in the area of rectangle formula.

$Area=2×1=2$

Hence, the area of the fifth rectangle is $2$ square units

Calculate the sum of areas of all the rectangles.

$4+5+2+0.5+2=13.5$

Hence, the area of the region above the $x$ -axis and under the graph of the function from $x=0$ to $x=5$ is $13.5$ square units.

Chapter 11.2, Problem 8E

Chapter 11.2, Problem 10E

Chapter 11 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 11.1 - Prob. 1QR Ch. 11.1 - Prob. 2QR Ch. 11.1 - Prob. 3QR Ch. 11.1 - Prob. 4QR Ch. 11.1 - Prob. 5QR Ch. 11.1 - Prob. 6QR Ch. 11.1 - Prob. 7QR Ch. 11.1 - Prob. 8QR Ch. 11.1 - Prob. 9QR Ch. 11.1 - Prob. 10QR

Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Prob. 15E Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Prob. 35E Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - Prob. 38E Ch. 11.1 - Prob. 39E Ch. 11.1 - Prob. 40E Ch. 11.1 - Prob. 41E Ch. 11.1 - Prob. 42E Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.1 - Prob. 47E Ch. 11.1 - Prob. 48E Ch. 11.1 - Prob. 49E Ch. 11.1 - Prob. 50E Ch. 11.1 - Prob. 51E Ch. 11.1 - Prob. 52E Ch. 11.1 - Prob. 53E Ch. 11.1 - Prob. 54E Ch. 11.1 - Prob. 55E Ch. 11.1 - Prob. 56E Ch. 11.1 - Prob. 57E Ch. 11.2 - Prob. 1QR Ch. 11.2 - Prob. 2QR Ch. 11.2 - Prob. 3QR Ch. 11.2 - Prob. 4QR Ch. 11.2 - Prob. 5QR Ch. 11.2 - Prob. 6QR Ch. 11.2 - Prob. 7QR Ch. 11.2 - Prob. 8QR Ch. 11.2 - Prob. 9QR Ch. 11.2 - Prob. 10QR Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Prob. 14E Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Prob. 32E Ch. 11.2 - Prob. 33E Ch. 11.2 - Prob. 34E Ch. 11.2 - Prob. 35E Ch. 11.2 - Prob. 36E Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.2 - Prob. 42E Ch. 11.2 - Prob. 43E Ch. 11.2 - Prob. 44E Ch. 11.2 - Prob. 45E Ch. 11.2 - Prob. 46E Ch. 11.2 - Prob. 47E Ch. 11.2 - Prob. 48E Ch. 11.2 - Prob. 49E Ch. 11.2 - Prob. 50E Ch. 11.2 - Prob. 51E Ch. 11.2 - Prob. 52E Ch. 11.2 - Prob. 53E Ch. 11.2 - Prob. 54E Ch. 11.2 - Prob. 55E Ch. 11.2 - Prob. 56E Ch. 11.2 - Prob. 58E Ch. 11.2 - Prob. 59E Ch. 11.2 - Prob. 60E Ch. 11.2 - Prob. 61E Ch. 11.2 - Prob. 62E Ch. 11.2 - Prob. 63E Ch. 11.2 - Prob. 64E Ch. 11.3 - Prob. 1QR Ch. 11.3 - Prob. 2QR Ch. 11.3 - Prob. 3QR Ch. 11.3 - Prob. 4QR Ch. 11.3 - Prob. 5QR Ch. 11.3 - Prob. 6QR Ch. 11.3 - Prob. 7QR Ch. 11.3 - Prob. 8QR Ch. 11.3 - Prob. 9QR Ch. 11.3 - Prob. 10QR Ch. 11.3 - Prob. 1E Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Prob. 4E Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Prob. 9E Ch. 11.3 - Prob. 10E Ch. 11.3 - Prob. 11E Ch. 11.3 - Prob. 12E Ch. 11.3 - Prob. 13E Ch. 11.3 - Prob. 14E Ch. 11.3 - Prob. 15E Ch. 11.3 - Prob. 16E Ch. 11.3 - Prob. 17E Ch. 11.3 - Prob. 18E Ch. 11.3 - Prob. 19E Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - Prob. 24E Ch. 11.3 - Prob. 25E Ch. 11.3 - Prob. 26E Ch. 11.3 - Prob. 27E Ch. 11.3 - Prob. 28E Ch. 11.3 - Prob. 29E Ch. 11.3 - Prob. 30E Ch. 11.3 - Prob. 31E Ch. 11.3 - Prob. 32E Ch. 11.3 - Prob. 33E Ch. 11.3 - Prob. 34E Ch. 11.3 - Prob. 35E Ch. 11.3 - Prob. 36E Ch. 11.3 - Prob. 37E Ch. 11.3 - Prob. 38E Ch. 11.3 - Prob. 39E Ch. 11.3 - Prob. 40E Ch. 11.3 - Prob. 41E Ch. 11.3 - Prob. 42E Ch. 11.3 - Prob. 43E Ch. 11.3 - Prob. 44E Ch. 11.3 - Prob. 45E Ch. 11.3 - Prob. 46E Ch. 11.3 - Prob. 47E Ch. 11.3 - Prob. 48E Ch. 11.3 - Prob. 49E Ch. 11.3 - Prob. 50E Ch. 11.3 - Prob. 51E Ch. 11.3 - Prob. 52E Ch. 11.3 - Prob. 53E Ch. 11.3 - Prob. 54E Ch. 11.3 - Prob. 55E Ch. 11.3 - Prob. 56E Ch. 11.3 - Prob. 57E Ch. 11.3 - Prob. 58E Ch. 11.3 - Prob. 59E Ch. 11.3 - Prob. 60E Ch. 11.3 - Prob. 61E Ch. 11.3 - Prob. 62E Ch. 11.3 - Prob. 63E Ch. 11.3 - Prob. 64E Ch. 11.3 - Prob. 65E Ch. 11.3 - Prob. 66E Ch. 11.3 - Prob. 67E Ch. 11.3 - Prob. 68E Ch. 11.3 - Prob. 69E Ch. 11.3 - Prob. 70E Ch. 11.3 - Prob. 71E Ch. 11.3 - Prob. 72E Ch. 11.3 - Prob. 73E Ch. 11.3 - Prob. 74E Ch. 11.3 - Prob. 75E Ch. 11.3 - Prob. 76E Ch. 11.3 - Prob. 77E Ch. 11.3 - Prob. 78E Ch. 11.3 - Prob. 79E Ch. 11.3 - Prob. 80E Ch. 11.3 - Prob. 81E Ch. 11.3 - Prob. 82E Ch. 11.3 - Prob. 83E Ch. 11.3 - Prob. 84E Ch. 11.3 - Prob. 85E Ch. 11.3 - Prob. 86E Ch. 11.3 - Prob. 88E Ch. 11.3 - Prob. 89E Ch. 11.3 - Prob. 90E Ch. 11.3 - Prob. 91E Ch. 11.3 - Prob. 92E Ch. 11.3 - Prob. 93E Ch. 11.4 - Prob. 1QR Ch. 11.4 - Prob. 2QR Ch. 11.4 - Prob. 3QR Ch. 11.4 - Prob. 4QR Ch. 11.4 - Prob. 5QR Ch. 11.4 - Prob. 6QR Ch. 11.4 - Prob. 7QR Ch. 11.4 - Prob. 8QR Ch. 11.4 - Prob. 9QR Ch. 11.4 - Prob. 10QR Ch. 11.4 - Prob. 1E Ch. 11.4 - Prob. 2E Ch. 11.4 - Prob. 3E Ch. 11.4 - Prob. 4E Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Prob. 7E Ch. 11.4 - Prob. 8E Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Prob. 12E Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Prob. 18E Ch. 11.4 - Prob. 19E Ch. 11.4 - Prob. 20E Ch. 11.4 - Prob. 21E Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - Prob. 24E Ch. 11.4 - Prob. 25E Ch. 11.4 - Prob. 26E Ch. 11.4 - Prob. 27E Ch. 11.4 - Prob. 28E Ch. 11.4 - Prob. 29E Ch. 11.4 - Prob. 30E Ch. 11.4 - Prob. 31E Ch. 11.4 - Prob. 32E Ch. 11.4 - Prob. 33E Ch. 11.4 - Prob. 34E Ch. 11.4 - Prob. 35E Ch. 11.4 - Prob. 36E Ch. 11.4 - Prob. 37E Ch. 11.4 - Prob. 38E Ch. 11.4 - Prob. 39E Ch. 11.4 - Prob. 40E Ch. 11.4 - Prob. 41E Ch. 11.4 - Prob. 42E Ch. 11.4 - Prob. 43E Ch. 11.4 - Prob. 44E Ch. 11.4 - Prob. 45E Ch. 11.4 - Prob. 46E Ch. 11.4 - Prob. 47E Ch. 11.4 - Prob. 48E Ch. 11.4 - Prob. 49E Ch. 11.4 - Prob. 51E Ch. 11.4 - Prob. 52E Ch. 11.4 - Prob. 54E Ch. 11.4 - Prob. 55E Ch. 11.4 - Prob. 56E Ch. 11.4 - Prob. 57E Ch. 11 - Prob. 1RE Ch. 11 - Prob. 2RE Ch. 11 - Prob. 3RE Ch. 11 - Prob. 4RE Ch. 11 - Prob. 5RE Ch. 11 - Prob. 6RE Ch. 11 - Prob. 7RE Ch. 11 - Prob. 8RE Ch. 11 - Prob. 9RE Ch. 11 - Prob. 10RE Ch. 11 - Prob. 11RE Ch. 11 - Prob. 12RE Ch. 11 - Prob. 13RE Ch. 11 - Prob. 14RE Ch. 11 - Prob. 15RE Ch. 11 - Prob. 16RE Ch. 11 - Prob. 17RE Ch. 11 - Prob. 18RE Ch. 11 - Prob. 19RE Ch. 11 - Prob. 20RE Ch. 11 - Prob. 21RE Ch. 11 - Prob. 22RE Ch. 11 - Prob. 23RE Ch. 11 - Prob. 24RE Ch. 11 - Prob. 25RE Ch. 11 - Prob. 26RE Ch. 11 - Prob. 27RE Ch. 11 - Prob. 28RE Ch. 11 - Prob. 29RE Ch. 11 - Prob. 30RE Ch. 11 - Prob. 31RE Ch. 11 - Prob. 32RE Ch. 11 - Prob. 33RE Ch. 11 - Prob. 34RE Ch. 11 - Prob. 35RE Ch. 11 - Prob. 36RE Ch. 11 - Prob. 37RE Ch. 11 - Prob. 38RE Ch. 11 - Prob. 40RE

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